Section: New Results

Aggregation of temporal graph series

A very natural and extensively used way to represent a dynamic network, where links change along time, is to build a graph series : the series of snapshots of the network taken at different time of its evolution. The way to do so is to aggregate all the contact information on a time window into a single graph : that is, we put an edge between u and v in the graph if they are in contact at least once during the considered time window. Doing so for disjoint windows of equal length which cover the whole period of study, we obtain a series of graphs representing the dynamics of the network. A question remain : how one should choose the length of the aggregation window? The problem is critical since depending on the choice made, the properties of the dynamic network are different and the conclusion derived from its analysis may change. We design a systematic method to estimate the maximum possible aggregation length. Up to our knowledge, this is the first method addressing the problem. It is based on activity rate of dynamic paths in the dynamics. On a dynamic path, only some time steps are used to move within the network. When the aggregation time is short, the activity rate of paths is close to zero and it tends to 1 when this time grow until the whole period of experiments. Between the two behaviors, we showed that there is a phase transition that we interpret as the moment when the properties of the dynamics are distorted because of the too long aggregation time.